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An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
Copyright policy ) Henry von Wahl; Thomas Richter; Christoph Lehrenfeld;
Henry von Wahl; Thomas Richter; Christoph Lehrenfeld;
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
Abstract We analyse a Eulerian finite element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations with the CutFEM approach using inf-sup stable Taylor–Hood elements for the spatial discretization. This is based on the method introduced by Lehrenfeld & Olshanskii (2019, A Eulerian finite element method for PDEs in time-dependent domains. ESAIM: M2AN, 53, 585–614) in the context of a scalar convection–diffusion problems on moving domains, and extended to the nonstationary Stokes problem on moving domains by Burman et al. (2019, arXiv:1910.03054 [math.NA]) using stabilized equal-order elements. The analysis includes the geometrical error made by integrating over approximated level set domains in the discrete CutFEM setting. The method is implemented and the theoretical results are illustrated using numerical examples.
Microsoft Academic Graph classification: Discretization Scalar (mathematics) Eulerian path Finite element method symbols.namesake Stokes problem symbols Applied mathematics Mathematics
Unfitted Finite Elements, Moving Domains, Applied Mathematics, General Mathematics, CutFEM, Numerical Analysis (math.NA), Computational Mathematics, Flow problems, FOS: Mathematics, Mathematics - Numerical Analysis
Unfitted Finite Elements, Moving Domains, Applied Mathematics, General Mathematics, CutFEM, Numerical Analysis (math.NA), Computational Mathematics, Flow problems, FOS: Mathematics, Mathematics - Numerical Analysis
Microsoft Academic Graph classification: Discretization Scalar (mathematics) Eulerian path Finite element method symbols.namesake Stokes problem symbols Applied mathematics Mathematics
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E. Burman, S. Frei and A. Massing. 'Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains'. In: Preprint (7th Oct. 2019). arXiv: 1910.03054v1 [math.NA].
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).11 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10% views 189 downloads 60 citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).11 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10% - 189views60downloads
citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
Popularity provided by BIP!influenceInfluence provided by BIP!
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Influence provided by BIP!impulseImpulse provided by BIP!
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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Abstract We analyse a Eulerian finite element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations with the CutFEM approach using inf-sup stable Taylor–Hood elements for the spatial discretization. This is based on the method introduced by Lehrenfeld & Olshanskii (2019, A Eulerian finite element method for PDEs in time-dependent domains. ESAIM: M2AN, 53, 585–614) in the context of a scalar convection–diffusion problems on moving domains, and extended to the nonstationary Stokes problem on moving domains by Burman et al. (2019, arXiv:1910.03054 [math.NA]) using stabilized equal-order elements. The analysis includes the geometrical error made by integrating over approximated level set domains in the discrete CutFEM setting. The method is implemented and the theoretical results are illustrated using numerical examples.
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